On relativistic theory of spinning and deformable particles

TL;DR

This paper develops a relativistic model for spinning and deformable particles using a 14-dimensional space that combines space-time with internal rotational and deformational degrees of freedom, enabling a unified description of extended particles.

Contribution

It introduces a 14-dimensional embedding space incorporating internal rotational and deformational variables, generalizes inertia and deformation tensors, and explores internal space properties within a relativistic framework.

Findings

Internal and external motions are independent, leading to split equations of motion.

A degenerate metric allows assigning a unique proper time to all points of the extended object.

Properties of the internal space are analyzed without spatial rotations.

Abstract

A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained 14-dimensional space is assumed to be an embedding one both for usual space-time and for 10-dimensional internal space of rotational and deformational variables. To describe such an internal space relativistic generaliza-tions of inertia and deformation tensors are given. Independence of internal and external motions from each other gives rise to splitting the equation of motion and some conditions for 14-dimensional metric. Using the 14-dimensional ideology makes possible to assign a unique proper time for all points of extended object, if the metric will be degenerate. Properties of an internal space are discussed in details in the case of absence of spatial rotations.